The second de Rham cohomology groups of nilpotent orbits in non-compact realforms of classical complex simple Lie algebras are explicitly computed.Furthermore, the first de Rham cohomology groups of nilpotent orbits innon-compact classical simple Lie algebras are computed; they are proven to bezero for nilpotent orbits in all the complex simple Lie algebras. A keycomponent in these computations is a description of the second and firstcohomology groups of homogeneous spaces of general connected Lie groups whichis obtained here.
展开▼
